In seismic applications, airgun source arrays are often used to generate acoustic output, which when reflected off of subsurface formations may be detected by associated seismic receivers. Such data is often used to build up an image of subsurface formations for assessing the likelihood of hydrocarbon production.
The low frequency output of marine airgun seismic sources is limited by the resonance frequency of the largest airgun volume in the source array. This oscillation frequency, also referred to as the fundamental bubble frequency, is given by the well-known Rayleigh-Willis formula:
                    f        =                  k          ⁢                                          ⁢                                                    (                                  1                  +                                      d                    /                    10                                                  )                                            5                /                6                                                                    (                                  P                  ·                  V                                )                                            1                /                3                                                                        (        1        )            Where f is the bubble frequency measured in Hertz, d is the source depth in meters, P is the firing pressure in psi (pound per square inch), V is the bubble volume in cubic inches and k is an empirical constant; k=506 matches well with measurements of conventional airguns.
Decreasing the bubble frequency requires a bigger bubble volume. The volume increase should be substantial since the bubble frequency is inversely proportional to the cube-root of the bubble volume. Some have recommended increasing the largest bubble volume as a way to increase the low frequency source output.
When airguns fire in a cluster, the resulting bubble frequency substantially equals that of a single gun of the combined volume. Earlier work on cluster design focused on maximizing the primary-to-bubble ratio of the resulting source signature. Such is the airgun cluster design in use today, where the clustered airguns are typically separated by less than one meter, and where the airgun bubbles coalesce into one non-spherical bubble. Other airguns in the source array are only weakly interacting, and the volume of these guns is normally chosen to achieve maximum destructive interference of the bubble amplitude of the overall source signature. This is known as a ‘tuned array’.